Numerical modelling of small groups of stone columns

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Vibro stone columns, installed using the vibro replacement technique, are a cost effective form of ground improvement for enhancing the bearing capacity and settlement characteristics of various soil types. Large groups of stone columns (such as used to support embankments) are conventionally modelled using the unit cell concept, which is based on an infinite grid of columns supporting an infinitely wide load area. Therefore all columns are equally confined on all sides and are subject to a constant increment of vertical stress with depth. The behaviour of small groups of stone columns supporting small area footings is quite complex as peripheral columns are subject to a loss of lateral confinement and the increment of vertical stress decays sharply with depth. This research is the first comprehensive three-dimensional numerical study of the factors affecting both the mechanisms of load transfer from columns to soil and the settlement performance of small column groups at working loads.
PLAXIS 3D Foundation is used for this research in conjunction with the advanced elasto-plastic Hardening Soil model, which is adopted for the parent soil and stone backfill. The soft soil modelled is that at Bothkennar, Scotland, the former UK geotechnical test bed. The influence of key design parameters such as area ratio, column length, stiffness, strength and installation effects upon the settlement performance and deformational behaviour of small groups of stone columns was investigated through a total of 45 numerical analyses.
The modelling has shown that the area ratio and column length have a significant influence on the settlement performance of stone columns. Moreover, they appear to be inter-dependent as the effect of column length becomes more pronounced at low area ratios. The influence of column confinement (i.e. increasing number of columns) was also found to have a positive influence on the settlement performance of small groups of stone columns. It was also shown that the influence of key design parameters upon the settlement performance of stone columns is dependent upon the mode of deformation.
New parameters called compression and punching ratios were defined to help identify three distinct mechanisms referred to as "punching", "block failure" and "bulging". The occurrence of these mechanisms was verified by analysing the distribution of total shear strain within columns and the surrounding soil and also examining the variation of stress and strain along the length of columns. It was found that area ratio and column length, rather than the number of columns, dictates the load transfer mechanism for small groups of stone columns.
A more in-depth analysis of the deformational behaviour reveals that some combination of punching and bulging occurs simultaneously, with one particular mode of deformation more influential for a given area ratio and column length. This is consistent with the finding that settlement improvement factors increase with column length for all configurations of columns and suggests that a unique critical length, as proposed by previous laboratory studies, does not exist for small groups of stone columns. The presence of a stiff crust, an important feature of soft soil stratigraphy not captured in the laboratory tests, was shown to have a significant influence upon the deformational behaviour of columns. The observation of a critical length from laboratory studies is shown in part to be due to the absence of a stiff crust (i.e. homogeneous soil samples) as columns are more susceptible to bulging in the upper layers and thus cannot transfer the applied load to their base.
The stress concentration ratios at the ground surface were also examined and it was found that they are related to the mode of deformation. Moreover, it was shown that stress concentration ratios vary considerably with column position and as such, do not uniquely reflect the settlement performance of stone columns. Instead, the stress concentration ratios with depth were noted and it was observed that they are constant with depth in the yielded sections of the column and decrease towards unity at the base of floating columns thereafter.
The numerical output in this thesis has been developed into a simplified design method which allows the settlement of a column group to be related to that of a unit cell with knowledge of the footing to column length ratio and the column length to layer thickness ratio (and thereby caters for floating column groups).

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